This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as the future event approaches. The threshold martingale introduced here measures the proportion of the forecast distribution lying below a threshold. In addition to being calibrated, a threshold martingale has quadratic variation that accumulates to a total determined by a quantile of the initial forecast distribution. Deviations from calibration or to- tal volatility signal problems in the underlying model. Calibration adjustments are well-known, and we augment these by introducing a martingale filter that improves volatility while guaranteeing smaller mean squared error. Thus, post-processing can rectify problems with calibration and volatility without revisiting the original forecast- ing model. We apply threshold martingales first to forecasts from simulated models and then to models that predict the winner in professional basketball games.

翻译：本文引入了一种马丁瓜, 其特征是不断演变的预测分布的两种特性。 对未来事件的预言表现为马丁瓜, 按顺序对预报进行三步更新, 以便在未来的事件接近时利用现有信息。 起始马丁瓜在此测量预测分布在临界值之下的比例。 除了校准外, 起始马丁瓜的二次变异会累积到由最初预测分布的四分位数决定的总和。 从校准到塔尔波动信号问题在基本模型中是众所周知的。 校准调整是众所周知的, 我们通过引入一个马丁瓜过滤器来增加这些变异性, 同时保证较小的平均平方差。 因此, 后处理可以纠正校准和波动问题, 而不重审原先的预测模型。 我们首先对模拟模型的预测进行阈值分数, 然后对在专业篮球比赛中预测获胜的模型进行预测。